Parts of the cryostat cool down to such cryogenic temperatures as
20 milliKelvin (0.02 K) using a technique called "3Helium - 4Helium
Dilution." For this reason another name for the cryostat is
"dilution refrigerator." This process relies on certain
thermodynamic characteristics of 3He (a rare helium isotope with 1 neutron) and 4He (the most abundant helium isotope, which has 2
neutrons). The 3He-4He dilution has the following phase diagram:

At temperatures below the triple point , the 3He-4He mixture will separate
into two liquid phases, divided by a phase boundary.

One phase we'll call the 3He rich phase, because it contains
mostly 3He. This corresponds to a point in the diagram
below and to the right of the triple point, along the
equilibrium line.

The second phase we'll call the 4He rich phase, because it
is mostly 4He -- it will, however, always be composed of at
least 6% 3He, no matter what temperature. This corresponds
to a point in the diagram below and to the left of the triple
point, along the equilibrium line.

The two phases are maintained in liquid-vapor form.
Since there is a boundary between both phases, extra energy is
required for particles to go from one phase to another.

A good example of this state would be what happens when you
mix together oil and water. If you maintain the mixture at a
high temperature they will stay mixed. But, if you were to
lower the temperature (this effect can be seen at room
temperature) the oil would separate from the water and float to
the top, giving you two different phases in the liquid
mixture. Not only that, but if you were to take a sample of
the oil you would find a small amount of water present and
vice-versa.

When you pump (we use a rotary pump) on the 4He rich phase you
will remove mostly 3He (a move to the left off the equilibrium line
in the diagram), destroying the equilibrium. To restore
equilibrium, 3He will have to cross the phase boundary from the 3He
rich side to the 4He rich side. However, it needs energy to
get past the boundary. The 3He rich phase will provide the 3He
and get the energy in the form of heat, from the walls of the mixing
chamber; the walls are in thermal contact with whatever you're
trying to cool down. Then the 3He will cross the phase
boundary and join the 4He rich phase, restoring equilibrium.
Finally, the atoms lost by the 3He rich phase are replenished by a
constantly circulating flow of 3He.

Another way of thinking about this process is in terms of
expansion. 4He is inert, in that it does not react with other
molecules and thermodynamically can be thought of as a vacuum in
some situations. Thus when the 3He moves from the 3He rich
phase to the 4He rich phase, it expands into an almost vacuum.
This expansion takes heat out of the walls of the mixing chamber,
reducing the temperature of whatever you're trying to cool.